Method and apparatus for color display with color transformation to improve perception for people with impaired color sight

ABSTRACT

A method and equipment for displaying a computer generated color image on which a color transformation is carried out so that a person with normal color vision is able to perceive the colors in a way which corresponds to the perception of a person with abnormal color vision. Use is made of this in order, on the basis of the user&#39;s own perception, or on the basis of an expert system, to adjust colors such that these comply with a preset distinguishability criterion which is matched to the ability of the particular target group of users, including users with normal color vision, to distinguish colors.

BACKGROUND OF THE INVENTION

The invention relates to a method and equipment for transforming thecolours generated by an image display system, in accordance with thelimitations which apply in respect of the perception of colours bypeople who have an abnormal form of colour vision, and the use thereoffor adaptation of the colour palette in a manner such that the coloursare easily distinguishable from one another for target groups having therelevant form of abnormal colour vision.

The invention relates in particular to a method and equipment fortransforming the colours of computer-generated images on an imagedisplay system, such as, for example, a cathode ray tube or LCD screen(liquid crystal display).

DESCRIPTION OF THE RELATED ART

People who have an abnormal form of colour vision, approximately 8% ofthe male population and 0.5% of the female population, do not perceivethe colours generated by an image display system in the standard manner.As a result certain functions of the image display system cannot beproperly utilised by this group of the population. In this contextconsideration can be given, for example, to the perception ofcolour-coded information in computer applications, such as controlpanels for industrial processes and electronically generatedgeographical and topographical maps.

SUMMARY OF THE INVENTION

One aim of the present invention is to provide a method with whichdevelopers of computer software and designers of visual informationsystems are able to perceive the colours they use in a manner whichcorresponds to the colour perception of a person who has abnormal colourvision. A further aim of the present invention is to provide a methodand equipment for transforming a set of colours in such a way that thedifferences between the colours comply with a pre-set distinguishabilitycriterion, taking account of the ability of the user to distinguishcolours, the various features being supported by a computational methodby means of which the set of colours concerned can automatically bemodified in accordance with the set distinguishability criterion.

To this end the method according to the invention is characterised inthat a data entry unit, connected to the image display system, forstoring digital colour specifications and system data in a colour memoryunit and memory unit is provided, as well as a computing unit, connectedto the data entry unit, for transformation of the digital colourspecifications of at least one pixel, as a function of the enteredcolour abnormality data and colour processing commands, comprising thefollowing steps:

a feeding of the digital colour specifications of the colour or set ofcolours to be transformed and of the colour abnormality and system datarequired for the transformation into the computing unit,

b calculation, with the aid of the computing unit, of three primaryphysiological colour signals for an observer with normal colour vision,

c calculation of a second set of three primary physiological coloursignals for an observer with abnormal colour vision, as specified by thecolour abnormality data,

d calculation of three new digital colour specifications for generationof colours which generate the same primary physiological colour signalsfor an observer with normal colour vision as the colour signalscalculated under c) for an observer with abnormal colour vision,

e calculation of trichromatic components X, Y and Z in the CIE colourspecification system which correspond to the new digital colourspecifications,

f assessment of the degree of colour difference in pairs of colourswithin the set of transformed colours, making use of calculations inaccordance with colour difference equations which already exist or arestill to be developed,

g selecting those colour differences from the colour differencescalculated under f) which do not meet a pre-set difference criterion andthen modifying the colours concerned, optionally with the assistance ofa computational method, such that said colours then comply with the setdifference criterion.

With computer-generated colours the luminance levels of the primarycolours are set by means of three colour-specific control signals. Eachcontrol signal is formed by an analog voltage originating from adigital-to-analog converter (DAC). An 8-bit DAC, with which analogcontrol signals are determined as a function of the digital colourspecifications, is frequently used. The digital colour specificationsare described by three numerals, which determine the magnitude of thecontributions of the three primary colours to the colours to begenerated. Assuming the generally used primary colours red (R), green(G) and blue (B), said digital colour specifications are indicated hereby numerical values N_(R), N_(G), and N_(B) respectively. With an 8-bitDAC these numerals vary from 0 to 255, so that a maximum of 256³different colours can be generated by combination of the three primarycolours of the image display system. Sets of 64 or 256 differentcolours, which can be made up from a palette of the said 256³ colours,can usually be rendered visible simultaneously by an image displaysystem.

The perception of colours by a person is initiated by absorption oflight in three different types of photoreceptors, which are alsoreferred to as the red, green and blue cones. The latter are mainlyeffective in the long wave, medium wave and short wave regions,respectively, of the visual spectrum, by means of spectral sensitivitiesl(λ), m(λ) and s(λ) of the photopigments matched to said regions. Theprimary physiological colour signals L, M and S generated by the conescan be described as the integral of the product of the spectralsensitivities concerned and the radiance of the light generated by theimage display system. Said radiance is determined by the digital colourspecifications and the spectral distribution of the primary coloursconcerned plus the so-called gamma functions, which describe therelationship between the relative radiances of the primary coloursc_(R), c_(G) and c_(B) as a function of the respective digital colourspecifications N_(R), N_(G) and N_(B).

In the case of an abnormal form of colour vision it can be that thereare not three but only two types of cones in the retina These so-calleddichromats can be subdivided into protanopes, characterised by the lackof red cones (or L receptors), deuteranopes, characterised by theabsence of green cones (or M receptors) and tritanopes, characterised bythe absence of blue cones (or S receptors). It can also occur that twoof the three types of cones have only very slight differences betweenthem as far as their spectral sensitivity is concerned. In the case ofthe so-called anomalous trichromats, a distinction is made betweenprotanomalopes, characterised by red cones having a spectral sensitivityl′(λ) which differs very little from that of the green cones, anddeuteranomalopes, having a spectral sensitivity m′(λ) which differs verylittle from that of the red cones.

As yet little is known about the tritanomalopes, characterised by anabnormal S receptor system. It is possible that in this case there ismerely a question of a reduced contribution by the S receptors, whichcan be described as a relative reduction in the number of S receptorscompared with the numbers of L and M receptors. For the time being thisassumption also forms the basis for the computational model used in theinvention for simulation of persons who have a tritanomaly. This group,that is to say tritanomalopes and tritanopes together, is relativelysmall; estimates vary from 0.005 to 0.1% of the population.

The invention will be explained in more detail with reference to theappended drawing, consisting of three figures.

In the drawing:

FIG. 1 shows, diagrammatically, equipment for displaying a colour image,

FIG. 2 shows the spectral sensitivity l(λ), m(λ) and s(λ) of the L, Mand S receptors, as well as abnormal forms thereof, l′(λ) and m′(λ),which are representative of, respectively, the protanomalous anddeuteranomalous form of abnormal colour vision, and

FIG. 3 shows the gamma functions of an image display system, in thiscase of a Philips Brilliance colour monitor (27-inch screen).

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 shows, diagrammatically, equipment for displaying colour imageson an image display system as well as the method for processing andtransforming colours. Data or commands are entered via the data entryunit (1) for processing and/or storage in a memory unit (2), a computingunit (3) and a colour memory unit (4). Digital input signals are fedfrom the colour memory unit to a digital-to-analog convertor (5). Thelatter is, for example, a conventional 8-bit DAC. In the example underconsideration, each of the three colour guns of a monitor (6) is driven,via said DAC (5), by an analog voltage of between 0 and 1 volt, which isadjusted using a numerical value between 0 and 255 in accordance withthe three digital colour specifications of the colours to be generated.In this way 256³ different colours can be produced by the combination ofthe three colour guns.

As is shown in FIG. 1, the computing unit (3) is connected to the dataentry unit (1), the memory unit (2) and the colour memory unit (4).Thus, commands which are given via the data entry unit (1) can beexecuted making use of data from the memory unit (2) and the colourmemory unit (4). The data which are fed to the computing unit (3) fromthe memory unit (2) relate to the colour abnormality data and to thecolorimetric data of the image display system, such as the spectral dataof the primary colours and the gamma functions, also referred to as thesystem profile. The data which the computing unit (3) obtains from thecolour memory unit (4) relate to that set of colours which belong to theimages to be generated on the image display system which is to betransformed. Following the transformation, the new digital colourspecifications of the set of colours are fed from the computing unit (3)to the colour memory unit (4).

As is likewise shown in FIG. 1, the data entry unit (1) is connected tothe memory unit (2), the computing unit (3) and the colour memory unit(4). Consequently, the commands can be given to the computing unit (3)and the data required for these can also be fed to the memory unit (2)and colour memory unit (4). The commands from the data entry unit (1) tothe computing unit (3) relate to the colour transformation to beperformed and to computational processing of the transformed coloursthus obtained, such as, for example, the calculation of specified colourdifferences.

When the method according to the invention is used to display a colourimage in accordance with the perception of a person who has abnormalcolour vision, the three primary physiological colour signals for normalcolour vision are calculated in accordance with

L=k∫L _(e)(λ)l(λ)dλ

M=k∫L _(e)(λ)m(λ)dλ

S=k∫L _(e)(λ)s(λ)dλ.  (1)

In these equations λ is the wavelength in nm and L_(e)(λ) the spectralradiance of the monitor in W.m⁻².sr⁻¹.nm⁻¹. The functions l(λ), m(λ) ands(λ) represent the spectral sensitivities of the three cones systems. Aspectral range of 400≦λ≦700 and an integration resolution of 2 nm cansuffice for the integration. The value of the constant k is of nofurther significance because this drops out in the subsequentcalculations.

Because a colour on the display of the monitor (6) is produced by acombination of the radiances of the red, green and blue primary colours,the radiance of the monitor L_(e)(λ) as a consequence of driving via theDAC (5) with the digital colour specifications N_(R), N_(G) and N_(B)can be described by:

L _(e)(λ)=R(λ)c _(R) +G(λ)c _(G) +B(λ)c _(B).  (2)

In this equation R(λ), G(λ) and B(λ) are the radiances of, respectively,the red, green and blue primary colours at the maximum input signal ofthe primary concerned. Said maxima are measured in the absence ofdriving of the other two primaries. Thus, for R(λ), N_(R)=255 andN_(G)=N_(B)=0. Similarly, for G(λ), N_(G)=255 and N_(R)=N_(B)=0, and forB(λ), N_(B)=255 and N_(R)=N_(G)=0. The variables c_(R), c_(G) and c_(B)represent the relative radiances of the three primary colours, that isto say standardised with respect to the respective maximum radiancesR(λ), G(λ) and B(λ). This implies that c_(R), c_(G) and c_(B) varybetween 0 and 1.

The values of c_(R), c_(G) and c_(B) as a function of the drive signalfrom the DAC progress in accordance with non-linear functions, the gammafunctions which have already been mentioned, an example of which is alsoshown in FIG. 3 of the drawing. The gamma functions can be determined bycalibration of the monitor (6) in accordance with an already knownprocedure in which the radiance of the primary colours is measured atvarious digital colour specifications (N). The data thus obtained, inthe form of the digital colour specifications N_(R), N_(G) and N_(B),with the relative radiances c_(R), c_(G) and c_(B) corresponding tothese, are stored in the memory unit (2). In the event that thecalibration data, such as the gamma functions, are not available asgiven, use is made of already existing standard data.

Following substitution of equation (2) in equation (1) the latter can berewritten as $\begin{matrix}{\begin{bmatrix}\begin{matrix}L \\M\end{matrix} \\S\end{bmatrix} = {{k\begin{bmatrix}{\int{{l(\lambda)}{R(\lambda)}{\lambda}}} & {\int{{l(\lambda)}{G(\lambda)}{\lambda}}} & {\int{{l(\lambda)}{B(\lambda)}{\lambda}}} \\{\int{{m(\lambda)}{R(\lambda)}{\lambda}}} & {\int{{m(\lambda)}{G(\lambda)}{\lambda}}} & {\int{{m(\lambda)}{B(\lambda)}{\lambda}}} \\{\int{{s(\lambda)}{R(\lambda)}{\lambda}}} & {\int{{s(\lambda)}{G(\lambda)}{\lambda}}} & {\int{{s(\lambda)}{B(\lambda)}{\lambda}}}\end{bmatrix}}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}} & (3)\end{matrix}$

or, in generic form, as $\begin{matrix}{\begin{bmatrix}\begin{matrix}L \\M\end{matrix} \\S\end{bmatrix} = {{k\begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}} & (4)\end{matrix}$

or, in abbreviated form, as $\begin{matrix}{\begin{bmatrix}\begin{matrix}L \\M\end{matrix} \\S\end{bmatrix} = {{{k\lbrack A\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}.}} & (5)\end{matrix}$

Using matrix A it is possible to calculate the corresponding values ofL, M and S for each combination of c_(R), c_(G) and c_(B). The converseis also possible, namely via the inverse matrix A⁻¹, in accordance with$\begin{matrix}{\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix} = {{{\frac{1}{k}\lbrack A\rbrack}^{- 1}\begin{bmatrix}\begin{matrix}L \\M\end{matrix} \\S\end{bmatrix}}.}} & (6)\end{matrix}$

Matrix A applies for normal colour vision. With persons who have a formof abnormal colour vision there is question of abnormal primaryphysiological colour signals, which are designated here by L′, M′ andS′, both for the dichromats and for the anomalous trichromats. For theabnormal colour vision L′, M′ and S′ are calculated in a manneranalogous to that for normal colour vision, in accordance with$\begin{matrix}{{\begin{bmatrix}\begin{matrix}L^{\prime} \\M^{\prime}\end{matrix} \\S^{\prime}\end{bmatrix} = {{k\left\lbrack A^{\prime} \right\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}},} & (7)\end{matrix}$

where the matrix A′, referred to as the deficiency matrix, is determinedby the colour abnormality data of the form of abnormal colour visionconcerned. Thus, for example, in the case of protanomalopes thedeficiency matrix A′ is calculated by replacing the spectral sensitivityl(λ) by l′(λ) in equation (3).

The simulation of the abnormal colour vision comes down to generating ina person having normal vision the abnormal primary physiological coloursignals L′, M′, S′ which are generated by the stimulus concerned in aperson with abnormal colour vision. The relative radiances of the imagedisplay system which are required for this are indicated by c′_(R),c′_(G) and c′_(B). Entering these in equation (5) gives $\begin{matrix}{\begin{bmatrix}\begin{matrix}L^{\prime} \\M^{\prime}\end{matrix} \\S^{\prime}\end{bmatrix} = {{{k\lbrack A\rbrack}\begin{bmatrix}\begin{matrix}c_{R}^{\prime} \\c_{G}^{\prime}\end{matrix} \\c_{B}^{\prime}\end{bmatrix}}.}} & (8)\end{matrix}$

By equating equation (7) and (8) it follows that $\begin{matrix}{\begin{bmatrix}\begin{matrix}c_{R}^{\prime} \\c_{G}^{\prime}\end{matrix} \\c_{B}^{\prime}\end{bmatrix} = {{{\lbrack A\rbrack^{- 1}\left\lbrack A^{\prime} \right\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}.}} & (9)\end{matrix}$

Given the values of c_(R), c_(G) and c_(B) of a colour, as calculatedusing equation (9), the relevant luminances of the primary colours aregenerated by entering the corresponding digital colour specificationsN_(R), N_(G) and N_(B), which are contained in the gamma functions ofthe image display system concerned.

In equation (9) the deficiency matrix A′ is calculated using equation(3), after entering the relevant colour abnormality data. For thisoperation use is made of the schedule of spectral sensitivities fornormal and abnormal colour vision shown in Table 1.

TABLE 1 Spectral sensitivities of the L, M and S receptors for normalcolour vision and the various forms of abnormal colour vision Type ofcolour Spectral sensitivities vision L receptor M receptor S receptorNormal l(λ) m(λ) s(λ) Protanope m(λ) m(λ) s(λ) Deuteranope l(λ) l(λ)s(λ) Tritanope l(λ) m(λ) l(λ), m(λ) Protanomalope l′(λ) m(λ) s(λ)Deuteranomalope l(λ) m′(λ) s(λ) Tritanomalope l(λ) m(λ) l(λ), m(λ), s(λ)

In the above schedule the abnormalities from normal colour vision areshown in bold. In this context it is assumed, in line with the generallyaccepted view, that abnormal colour vision is not associated with a lossof receptors. This means, as can also be seen from the table, that inthe case of the protanope the pigment of the L receptors is replaced bythe pigment of the M receptors, whilst the converse applies for thedeuteranope. In the case of the anomalous trichromats, in the L and Mreceptors the normal pigments, with spectral sensitivities l(λ) andm(λ), are replaced by pigments with the abnormal spectral sensitivitiesl′(λ) and m′(λ). Little is known about tritanomaly. For the time beingit is assumed that no abnormal pigments are involved here but that thereis exclusively replacement of S pigment by L and M pigment, specificallyto an equal degree. For the tritanopes this applies for all receptors,resulting in two equal fractions of S receptors, filled with L pigmentand M pigment respectively. For the tritanomalopes the abnormality isfor the time being described by assuming that a proportion of the Sreceptors, estimated as ⅓, are still provided with the original Spigment, resulting in an equal contribution by the three differentspectral sensitivities l(λ), m(λ) and s(λ) to the colour signal S′ ofthe abnormal S receptor system.

In line with the literature it is assumed that, as in the case of normalcolour vision, the primary physiological colour signals in the case ofabnormal colour vision are identical to one another in the case of whitelight, i.e. L′_(w)=M′_(w)=S′_(w). What is concerned here is theso-called ‘equal energy’ white, which is characterised by a spectraldistribution which does not change over the entire visual spectrum.

The change from normal to abnormal colour vision can be calculated foreach colour by replacing three of the coefficients a₁-a₉ in the standardmatrix A by the three coefficients which result on replacement of thenormal pigment by the pigment of the abnormal receptor system concerned.On the basis of the schedule shown in Table 1, this results in 6different deficiency matrices, i.e. for the protanope, theprotanomalope, the deuteranope, the deuteranomalope, the tritanope andthe tritanomalope.

For normal colour vision $\begin{matrix}{\lbrack A\rbrack = {\begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}.}} & (10)\end{matrix}$

In the case of the protanope the pigment of the L receptor is replacedby that of the M receptor, which results in the deficiency matrix[A′]_(P) in accordance with $\begin{matrix}{{\left\lbrack A^{\prime} \right\rbrack_{P} = \begin{bmatrix}a_{4} & a_{5} & a_{6} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},} & (11)\end{matrix}$

with the feature that the normal coefficients a₁-a₃ have been replacedby the likewise normal coefficients a₄-a₆.

In the case of the protanomalopes the pigment of the L receptor isreplaced by that of the L′ receptor, which results in the deficiencymatrix [A′]_(Pa) in accordance with $\begin{matrix}{{\left\lbrack A^{\prime} \right\rbrack_{P\quad a} = \begin{bmatrix}a_{1}^{\prime} & a_{2}^{\prime} & a_{3}^{\prime} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},} & (12)\end{matrix}$

with the feature that the normal coefficients a₁-a₃ have been replacedby the abnormal coefficients a′₁-a′₃, as calculated by replacing l(λ) byl′(λ) in equation 3.

In the case of the deuteranope the pigment of the M receptor is replacedby that of the L receptor, which results in the deficiency matrix[A′]_(D) in accordance with $\begin{matrix}{{\left\lbrack A^{\prime} \right\rbrack_{D} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{1} & a_{2} & a_{3} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},} & (13)\end{matrix}$

with the feature that the normal coefficients a₄-a₆ have been replacedby the likewise normal coefficients a₁-a₃.

In the case of the deuteranomalope the pigment of the M receptor isreplaced by that of the M′ receptor, which results in the deficiencymatrix [A′]_(Da) in accordance with $\begin{matrix}{{\left\lbrack A^{\prime} \right\rbrack_{Da} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4}^{\prime} & a_{5}^{\prime} & a_{6}^{\prime} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},} & (14)\end{matrix}$

with the feature that the normal coefficients a₄-a₆ have been replacedby the abnormal coefficients a′₄-a′₆ as calculated by replacing m(λ) bym′(λ) in equation (3).

For the tritanopes the S receptors are represented by equal numbers of Mand L receptors, which results in the deficiency matrix [A′]_(T) inaccordance with $\begin{matrix}{{\left\lbrack A^{\prime} \right\rbrack_{T} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\{{1/2}\left( {a_{1} + a_{4}} \right)} & {{1/2}\left( {a_{2} + a_{5}} \right)} & {{1/2}\left( {a_{3} + a_{6}} \right)}\end{bmatrix}},} & (15)\end{matrix}$

with the feature that the normal coefficients a₇-a₉ have been replacedby the shown combinations of two normal coefficients.

For the tritanomalopes the S receptors are represented by equal numbersof L, M and S receptors, which results in the deficiency matrix[A′]_(Ta) in accordance with $\begin{matrix}{{\left\lbrack A^{\prime} \right\rbrack_{Ta} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\{{1/3}\left( {a_{1} + a_{4} + a_{7}} \right)} & {{1/3}\left( {a_{2} + a_{5} + a_{8}} \right)} & {{1/3}\left( {a_{3} + a_{6} + a_{9}} \right)}\end{bmatrix}},} & (16)\end{matrix}$

with the feature that the normal coefficients a₇-a₉ have been replacedby the shown combinations of three normal coefficients.

The values of the coefficients in both the normal matrix A and in thevarious types of deficiency matrix A′ are determined not only by thecolour abnormality data but also by the spectral distribution of theprimary colours of the image display system. On changing the primarycolours of the image display system, all coefficients will thus alsohave to change.

The possibility of perceiving colours in the same way as these areperceived in the case of abnormal colour vision is utilised to detectthe combinations in a given set of colours which are indistinguishableor poorly distinguishable by a person with the particular form ofabnormal colour vision. Use is made of standard colorimetric equationsto establish a quantitative criterion for the degree to which twocolours differ from one another. In these equations use is made of thestandardised X Y Z colour specification system from the CommissionInternationale d'Eclairage (CIE). Analogously to equation (1) theparameters X, Y and Z, the so-called trichromatic components, can bedefined as follows

X=K∫L _(e)(λ){overscore (x)}(λ)dλ

Y=K∫L _(e)(λ){overscore (y)}(λ)dλ

Z=K∫L _(e)(λ){overscore (z)}(λ)dλ,  (17)

where L_(e) is the spectral radiance of the stimulus concerned and{overscore (x)}(λ), {overscore (y)}(λ) and {overscore (z)}(λ) are thethree spectral sensitivity functions of the CIE standard observer, theso-called CIE colorimetric functions. The constant K corresponds to 638lm/W. The parameter Y, expressed in cd/m², is used as standard for thebrightness (luminance) of a visual stimulus.

To transform a colour stimulus from the LMS domain to the XYZ domain, atransformation from LMS to RGB is first carried out, as described byequation (6), followed by a transformation from RGB to XYZ. Thistransformation is carried out in a manner analogous to that describedpreviously for the transformation of RGB to LMS, i.e. by replacing themaximum radiances of the primary colours, r(λ), g(λ) and b(λ), in matrixA by the CIE colorimetric functions, {overscore (x)}(λ), {overscore(y)}(λ) and {overscore (z)}(λ), respectively, giving as a result$\begin{matrix}{{\begin{bmatrix}\begin{matrix}X \\Y\end{matrix} \\Z\end{bmatrix} = {{K\lbrack B\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}},} & (18)\end{matrix}$

where K is the same constant as in (17) and where matrix B is calculatedusing $\begin{matrix}{\lbrack B\rbrack = {\begin{bmatrix}{\int{{r(\lambda)}{\overset{\_}{x}(\lambda)}{\lambda}}} & {\int{{g(\lambda)}{\overset{\_}{x}(\lambda)}{\lambda}}} & {\int{{b(\lambda)}{\overset{\_}{x}(\lambda)}{\lambda}}} \\{\int{{r(\lambda)}{\overset{\_}{y}(\lambda)}{\lambda}}} & {\int{{g(\lambda)}{\overset{\_}{y}(\lambda)}{\lambda}}} & {\int{{b(\lambda)}{\overset{\_}{y}(\lambda)}{\lambda}}} \\{\int{{r(\lambda)}{\overset{\_}{z}(\lambda)}{\lambda}}} & {\int{{g(\lambda)}{\overset{\_}{z}(\lambda)}{\lambda}}} & {\int{{b(\lambda)}{\overset{\_}{z}(\lambda)}{\lambda}}}\end{bmatrix}.}} & (19)\end{matrix}$

After specification of the colours in terms of the CIE units X, Y and Z,the latter are then transformed to coordinates of a uniform colourspace. In such a space the dimensions X, Y and Z are transformed todimensions which give a better description in terms of colourperception. In a uniform colour space the distances between colours, asdefined in the colour coordinates concerned, are representative of thedifferences corresponding thereto in the perception of the colours. TheCIE defines two such uniform colour spaces, CIELUV and CIELAB. Theassociated colour difference equations were developed for reflectedcolours and consequently are not optimum for use with theself-illuminating colours on a monitor. There are also yet furthercolour difference equations, which are specifically matched to thecolours of the monitor, under development. However, there is nogenerally accepted standard as yet. For the time being, the inventiontherefore makes use of the CIELUV equation, but also offers thepossibility of introducing other equations as well, the variables ofwhich can be derived to transformations of X, Y and Z. Such equationsare stored in the memory unit (2).

The parameters used for calculation of colour differences according tothe CIELUV system are the associated u′ and v′ colour coordinates and aparameter L*, which is representative of the relative luminance of thecolour stimulus. The colour coordinates u′ and v′ are defined as follows$\begin{matrix}{{u^{\prime} = \frac{4X}{X + {15Y} + {3Z}}}{v^{\prime} = \frac{9Y}{X + {15Y} + {3Z}}}} & (20)\end{matrix}$

When calculating a colour difference, the colours concerned are firststandardised to the brightest colour in the image. For a monitor that isthe brightest white, as characterised by the digital colourspecifications N_(R)=N_(G)=N_(B)=255. The relevant trichromaticcomponents are indicated by X_(n)=Y_(n)=Z_(n), with the colourcoordinates corresponding thereto, u′_(n) and v′_(n), specified as$\begin{matrix}{{u_{n}^{\prime} = \frac{4X_{n}}{X_{n} + {15Y_{n}} + {3Z_{n}}}}{v_{n}^{\prime} = \frac{9Y_{n}}{X_{n} + {15Y_{n}} + {3Z_{n}}}}} & (21)\end{matrix}$

According to the CIELUV system, a colour is described as follows

L*=116(Y/Y _(n))^(⅓)−16

u*=13L*(u′−u _(n)′)

v*=13L*(u′−u _(n)′)  (22)

The difference between two colours, ΔE*_(uv), is calculated using$\begin{matrix}{{\Delta \quad E_{uv}^{*}} = \sqrt{\left( {L_{1}^{*} - L_{2}^{*}} \right)^{2} + \left( {u_{1}^{*} - u_{2}^{*}} \right)^{2} + \left( {v_{1}^{*} - v_{2}^{*}} \right)^{2}}} & (23)\end{matrix}$

This equation is modified for the case where Y/Y_(n)≦0.0089. In thiscase L* is calculated using L*=903.3 (Y/Y_(n)).

In order to be able to determine which combinations of colours do notmeet a preset criterion of ΔE*_(uv), the invention has a computerprogram, to be executed by the computing unit (3), with which this canbe investigated. With this program all colour differences which canarise within a specific set of colours are calculated, i.e. ½ (n²−n)combinations for a set of n colours. In the invention this computerprogram is used on the set of colours which has been transformed fromthe LMS colour space of normal colour vision to the L′M′S′ colour spaceof the abnormal colour vision. Table 2 shows the result of such acalculation, both before and after the transformation from normal colourvision to abnormal colour vision. The table relates to colours in acolour set of 7 equally bright colours (Y=12 cd/m²).

TABLE 2 Colour differences, ΔE*_(u′v′), within a set of 7 colours ofequal brightness (Y = 12 cd/m²) for normal colour vision (shaded cells)and for the abnormal colour vision as occurs in the case of protanomaly,respectively. The numerals printed in bold relate to colour differencesfor which ΔE*_(uv) ≦ 30. The XYZ specifications of the colours are givenin the first row

In the invention colours which do not meet the desired ΔE*_(uv)criterion are detected automatically. This is shown in Table 2 for thecriterion ΔE*_(uv)≦30. The colour combinations concerned are printed inbold, from which it can be seen that whereas in the case of normalcolour vision (shaded cells) there is question only of one combinationwhich does not meet the criterion, there is question of five suchcombinations in the case of abnormal colour vision.

In order still to be able to achieve compliance in those cases in whichthe required difference criterion is not met, new digital colourspecifications can be provided using the data entry unit (1) and theeffect thereof rendered visible via the image display system. Ifnecessary this process can be repeated until there is compliance withthe set difference criterion. With this method of colour adaptation tothe requirements of the user with abnormal colour vision, use can alsobe made of assistance from a computational method. Such a method is alsoimplemented in the invention. With this method the colour combinationswhich do not comply with a preset difference criterion are detected andthe distance between the colours concerned is then increased until therequired criterion is met. To this end the distance is maximised in theprojected u*,v* plane of the CIELUV colour space, followed, ifnecessary, by a further enlargement of the colour difference by means ofenlarging the difference along the L* axis. After the result from theexpert system has been rendered visible, this can optionally also befurther processed by manual input of new digital colour specifications.

What is claimed is:
 1. Method for displaying a colour image using animage display system comprising an image plane with pixels, a data entryunit, connected to the image display system, for input by a user ofdigital colour specifications and calibration data to a colour memoryunit and memory unit, and a computing unit, connected to the data entryunit, for the transformation and processing of the digital colourspecifications, as a function of colour abnormality data and colourprocessing commands selected by the user, comprising the followingsteps: a) feeding of the digital colour specifications of the colour orset of colours to be transformed and of the colour abnormality andsystem data required for the transformation into the computing unit, b)calculation, with the aid of the computing unit, of three primaryphysiological colour signals for an observer with normal colour vision,c) calculation of a second set of three primary physiological coloursignals for an observer with abnormal colour vision, as specified by thecolour abnormality data, d) calculation of three new digital colourspecifications for generation of colours which generate the same primaryphysiological colour signals for an observer with normal colour visionas the colour signals calculated under c) for an observer with abnormalcolor vision, e) calculation of trichromatic components X, Y and Z inthe CIE colour specification system which correspond to the new digitalcolour specifications, f) assessment of the degree of colour differencein pairs of colours within the set of transformed colours, making use ofcalculations in accordance with predetermined colour differenceequations, g) selecting those color differences from the colourdifferences calculated under f) which do not meet a pre-set differencecriterion and then modifying the colours concerned, optionally with theassistance of a computational method, such that said colours then complywith the set difference criterion, prior to carrying out step a, thecolorimetric data required for calculation of the radiances of theprimary colours have been collected and stored in a memory unitconnected to the computing unit, wherein the colorimetric data of theimage display system, also referred to as the profile of the system, areobtained by measuring the spectral distribution of the primary coloursof the image display system and the relevant gamma functions, whichindicate the relationship between digital input signals and relativeradiances of the primary colours.
 2. Method according to claim 1,wherein in step b the first three primary physiological colour signalsare calculated using L=k∫L _(e)(λ)l(λ)dλ M=k∫L _(e)(λ)m(λ)dλ S=k∫L_(e)(λ)s(λ)dλ, where: L_(e)(λ) is the radiance of the pixel inW.m⁻².sr⁻¹.nm⁻¹, l(λ), m(λ) and s(λ) represent the spectral sensitivityof the three receptor systems, k is a constant which subsequently dropsout in the calculations and λ is the wavelength, which can vary between400 and 800 nm.
 3. Method according to claim 2, wherein thephysiological primary colours L, M and S are calculated using${\begin{bmatrix}\begin{matrix}L \\M\end{matrix} \\S\end{bmatrix} = {{k\lbrack A\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}},$

where [A] consists of 9 coefficients, defined as $\begin{matrix}{\lbrack A\rbrack = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}} & (26)\end{matrix}$

and a₁-a₉ are calculated using ${\lbrack A\rbrack = \begin{bmatrix}{\int{{l(\lambda)}{R(\lambda)}{\lambda}}} & {\int{{l(\lambda)}{G(\lambda)}{\lambda}}} & {\int{{l(\lambda)}{B(\lambda)}{\lambda}}} \\{\int{{m(\lambda)}{R(\lambda)}{\lambda}}} & {\int{{m(\lambda)}{G(\lambda)}{\lambda}}} & {\int{{m(\lambda)}{B(\lambda)}{\lambda}}} \\{\int{{s(\lambda)}{R(\lambda)}{\lambda}}} & {\int{{s(\lambda)}{G(\lambda)}{\lambda}}} & {\int{{s(\lambda)}{B(\lambda)}{\lambda}}}\end{bmatrix}},$

where R(λ), G(λ) and B(λ) represent the maximum radiances of the primarycolours of the image display system.
 4. Method according to claim 3,wherein step c comprises the calculation of the physiological primarycolours L′, M′ and S′ for a person with abnormal colour vision, inaccordance with ${\begin{bmatrix}\begin{matrix}L^{\prime} \\M^{\prime}\end{matrix} \\S^{\prime}\end{bmatrix} = {{k\left\lbrack A^{\prime} \right\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}},$

where the matrix A′, referred to as the deficiency matrix, is determinedby the colour abnormality data for the particular form of abnormalcolour vision and accordingly can assume the following forms:${\left\lbrack A^{\prime} \right\rbrack_{P} = \begin{bmatrix}a_{4} & a_{5} & a_{6} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},$

with the feature that the normal coefficients a₁-a₃ have been replacedby the likewise normal coefficients a₄-a₆,${\left\lbrack A^{\prime} \right\rbrack_{P\quad a} = \begin{bmatrix}a_{1}^{\prime} & a_{2}^{\prime} & a_{3}^{\prime} \\a_{4} & a_{5} & a_{6} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},$

with the feature that the normal coefficients a₁-a₃ have been replacedby the abnormal coefficients a′₁-a′₃, as calculated by replacing l(λ) byl′(λ) in matrix [A],${\left\lbrack A^{\prime} \right\rbrack_{D} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{1} & a_{2} & a_{3} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},$

with the feature that the normal coefficients a₄-a₆ have been replacedby the likewise normal coefficients a₁-a₃,${\left\lbrack A^{\prime} \right\rbrack_{Da} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4}^{\prime} & a_{5}^{\prime} & a_{6}^{\prime} \\a_{7} & a_{8} & a_{9}\end{bmatrix}},$

with the feature that the normal coefficients a₄-a₆ have been replacedby the abnormal coefficients a′₄-a′₆, as calculated by replacing m(λ) bym′(λ) in matrix [A],${\left\lbrack A^{\prime} \right\rbrack_{T} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\{{1/2}\left( {a_{1} + a_{4}} \right)} & {{1/2}\left( {a_{2} + a_{5}} \right)} & {{1/2}\left( {a_{3} + a_{6}} \right)}\end{bmatrix}},$

with the feature that the normal coefficients a₇-a₉ have been replacedby the shown combinations of two, likewise normal coefficients,${\left\lbrack A^{\prime} \right\rbrack_{Ta} = \begin{bmatrix}a_{1} & a_{2} & a_{3} \\a_{4} & a_{5} & a_{6} \\{{1/3}\left( {a_{1} + a_{4} + a_{7}} \right)} & {{1/3}\left( {a_{2} + a_{5} + a_{8}} \right)} & {{1/3}\left( {a_{3} + a_{6} + a_{9}} \right)}\end{bmatrix}},$

with the feature that the normal coefficients a₇-a₉ have been replacedby the shown combinations of three, likewise normal coefficients. 5.Method according to claim 4, wherein step d comprises calculation of thevalues of the primary colours c′_(R), c′_(G) and c′_(B) in accordancewith ${\begin{bmatrix}\begin{matrix}c_{R}^{\prime} \\c_{G}^{\prime}\end{matrix} \\c_{B}^{\prime}\end{bmatrix} = {{\lbrack A\rbrack^{- 1}\left\lbrack A^{\prime} \right\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}},$

where A′ is calculated with reference to claim
 5. 6. Method according toclaim 5, wherein step e comprises calculation of the matrix B, whichapplies for the transformation of XYZ to the RGB domain in accordancewith ${\begin{bmatrix}\begin{matrix}X \\Y\end{matrix} \\Z\end{bmatrix} = {{K\lbrack B\rbrack}\begin{bmatrix}\begin{matrix}c_{R} \\c_{G}\end{matrix} \\c_{B}\end{bmatrix}}},$

where the constant K corresponds to 683 lm/W and matrix B is calculatedusing ${\lbrack B\rbrack = \begin{bmatrix}{\int{{r(\lambda)}{\overset{\_}{x}(\lambda)}{\lambda}}} & {\int{{g(\lambda)}{\overset{\_}{x}(\lambda)}{\lambda}}} & {\int{{b(\lambda)}{\overset{\_}{x}(\lambda)}{\lambda}}} \\{\int{{r(\lambda)}{\overset{\_}{y}(\lambda)}{\lambda}}} & {\int{{g(\lambda)}{\overset{\_}{y}(\lambda)}{\lambda}}} & {\int{{b(\lambda)}{\overset{\_}{y}(\lambda)}{\lambda}}} \\{\int{{r(\lambda)}{\overset{\_}{z}(\lambda)}{\lambda}}} & {\int{{g(\lambda)}{\overset{\_}{z}(\lambda)}{\lambda}}} & {\int{{b(\lambda)}{\overset{\_}{z}(\lambda)}{\lambda}}}\end{bmatrix}},$

where {overscore (x)}(λ), {overscore (y)}(λ) and {overscore (z)}(λ) arethe CIE colorimetric functions.
 7. A Method according to claim 6,wherein step f comprises calculation of colour differences of allcombinations of two colours within the transformed colour set, makinguse of an arbitrary colour difference equation, such as, for example,the equation according to the CIELUV system, with which the colourdifference ΔE*_(uv) is calculated in accordance with${{\Delta \quad E_{uv}^{*}} = \sqrt{\left( {L_{1}^{*} - L_{2}^{*}} \right)^{2} + \left( {u_{1}^{*} - u_{2}^{*}} \right)^{2} + \left( {v_{1}^{*} - v_{2}^{*}} \right)^{2}}},$

where L*=116(Y/Y _(n))^(⅓)−16 u*=13L*(u′−u′ _(n)) v*=13L*(u′−u′ _(n))$u^{\prime} = \frac{4X}{X + {15Y} + {3Z}}$$v^{\prime} = \frac{9X}{X + {15Y} + {3Z}}$$u_{n}^{\prime} = \frac{4X_{n}}{X_{n} + {15Y_{n}} + {3Z_{n}}}$${v_{n}^{\prime} = \frac{9Y_{n}}{X_{n} + {15Y_{n}} + {3Z_{n}}}},$

where X, Y, Z are the CIE trichromatic components, subscripts 1 and 2relate to two different colours and subscript n relates to the brightestcolour white of the image display system.
 8. Method according to claim7, wherein step g comprises registering the colour differences which donot comply with a criterion set by the user and then changing thecolours concerned such that these do comply with the set criterion,either manually, in interaction with the user, or automatically, on thebasis of a computational method.
 9. Equipment for carrying out themethod according to claim 1, comprising a memory unit (2), a computingunit (3) and a colour memory unit (4) as well as a data entry unit (1).10. Method for displaying a colour image using an image display systemcomprising an image plane with pixels, a data entry unit, connected tothe image display system, for input by a user of digital colourspecifications and calibration data to a colour memory unit and memoryunit, and a computing unit, connected to the data entry unit, for thetransformation and processing of the digital colour specifications, as afunction of colour abnormality data and colour processing commandsselected by the user, comprising the following steps: a) feeding of thedigital colour specification N_(R), N_(G) or N_(B) of the colour of setof colours to be transformed and of the colour abnormality and systemdata required for the transmission into the computing unit; b)determining with the aid of the computing and/or memory unit, thecoefficients [A] of a first set of three primary physiological coloursignals L, M, S for an observer with normal colour vision; c)determining of the coefficients [A′] of a second set of three primaryphysiological colour signals L′,M′,S′ abnormality data; d) calculationof three new digital colour specifications N_(R),N_(G) or N_(B) forgeneration of colours which generate the same primary physiologicalcolour signals L′,M′,S′ for an observer with normal colour vision as thesecond set of primary physiological using the coefficient [A], [A′],determined under steps a. and b., colour signals under c. for anobserver with abnormal colour vision; e) calculation of trichromaticcomponents X, Y and Z in the CIE colour specification system whichcorrespond to the new digital colour specifications; f) assessment ofthe degree of colour difference in pairs of colours within the set oftransformed colours, making use of calculations in accordance withpredetermined colour difference equations; and g) selecting those colourdifferences from the colour differences calculating under f. which donot meet a pre-set difference criterion and then modifying the coloursconcerned, optionally with the assistance of a computational method,such that said colours then comply with the set difference criterion.11. Method according to claim 10, characterized in that, prior tocarrying out step a, the colorimetric data required for calculation ofthe radiances of the primary colours have been collected and stored in amemory unit connected to the computing unit.
 12. Method according toclaim 10, wherein the colorimetric data of the image display system,also referred to as the profile of the system, are obtained by measuringthe spectral distribution of the primary colours of the image displaysystem and the relevant gamma functions, which indicate the relationshipbetween digital input signals and relative radiances of the primarycolours.
 13. Equipment for carrying out the method according to claim10, comprising a memory unit (2), a computing unit (3) and a colourmemory unit (4) as well as a data entry unit (1).